Home
Class 12
MATHS
The function f(x) = (4-x^(2))/(4x-x^(3))...

The function `f(x) = (4-x^(2))/(4x-x^(3))` is

A

discontinuous at only one point

B

discontinuous at exactly two points

C

discontinuous at exactly three points

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
C
We have, `f(x) = (4-x^(2))/(4x-x^(2))=((4-x^(2)))/(x(4-x^(2)))`
` = ((4-x^(2)))/(x(2^(2)-x^(2))) = (4-x^(2))/(x(2+x)(2-x))`
Clearly , `f(x)` is discontinuous at exactly three points `x = 0, x = - 2` and `x = 2`.
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    NCERT EXEMPLAR|Exercise Application Of Integrals|68 Videos

  • DETERMINANTS

    NCERT EXEMPLAR|Exercise Determinants|58 Videos

Similar Questions

Explore conceptually related problems

The function f(x)=(4-x^(2))/(4x-x^(3)) a)discontinuous at only one point b) discontinuous exactly at two point b) c)discontinuous exactly at two points of these

The function f(x)=(4-x^(2))/(|4x-x^(3)|) is (a)discontinuous at only one point (b) Discontinuous at exactly two points (c) Discontinuous at exactly three points none of these

Range of the function f(x)=(x-2)/(x^(2)-4x+3) is

For what values of x the function f(x)= x^(4)-4x^(3)+4x^(2)+40 is monotonically increasing ?

Find the asymptotes, intercepts and sketch the graph of the function f(x)=(x^2-4)/(x^3-4x^2)

Find the domain and range function f(x) =(x^(2)-3x+2)/(x^(2)-4x+3) .

For what values of x the function f(x)=x^(4)-4x^(3)+4x^(2)+40 is monotonic decreasing?

Find the domain of the function f(x)=(x^2-4)/(x-4)

The function f(x) = 3x^(4) + 4x^(3) – 12x^(2) – 7 is

Range of the function f(x)=(x-2)/(x^(3)+2x^(2)-4x-8) .is equal to

NCERT EXEMPLAR-CONTINUITY AND DIFFERENTIABILITY-Continuity And Differentiability
  1. Find the values of (dy)/(dx), if y = x^(tanx)+sqrt((x^(2)+1)/(2)).

    Text Solution

    |

  2. If f(x) = 2x and g(x) = (x^(2))/(2)+1 , then which of the following ...

    Text Solution

    |

  3. The function f(x) = (4-x^(2))/(4x-x^(3)) is

    Text Solution

    |

  4. The set of points where the function f given by f(x) - |2x-1| sinx ...

    Text Solution

    |

  5. The function f(x) =cot x is discontinuous on set

    Text Solution

    |

  6. The function f(x) = e^(|x|) is

    Text Solution

    |

  7. If f(x) = x^(2)sin'(1)/(x), where x ne 0, then the value of the functi...

    Text Solution

    |

  8. If f(x)=[{:(mx+1,if x le (pi)/(2)),(sinx+n,ifxgt(pi)/(2)):} is contin...

    Text Solution

    |

  9. If f(x) = |sinx|, then

    Text Solution

    |

  10. If y = log ((1-x^(2))/(1+x^(2))), then (dy)/(dx) is equal to

    Text Solution

    |

  11. If y = sqrt(sinx+y), then (dy)/(dx) is equal to

    Text Solution

    |

  12. The derivative of cos^(-1)(2x^(2)-1) w.r.t. cos^(-1) is

    Text Solution

    |

  13. If x = t^(2) and y = t^(3), then (d^(2)y)/(dx^(2)) is equal to

    Text Solution

    |

  14. The value of c in Rolle's theorem for the function f(x) = x^(3) - 3...

    Text Solution

    |

  15. For the function f(x) = x + 1/x, x in [1,3] , the value of c for me...

    Text Solution

    |

  16. An example of a function which is continuous every where but fails to...

    Text Solution

    |

  17. Derivative of x^(2) w.r.t. x^(3) is "……."

    Text Solution

    |

  18. If f(x) = |cosx|, then f'(pi/4) is equal to "……."

    Text Solution

    |

  19. For the curve sqrt(x) + sqrt(y) = 1, (dy)/(dx) at (1/4,1/4) is "……….".

    Text Solution

    |

  20. Rolle's theorem is applicable for the function f(x) = |x-1| in [0,2].

    Text Solution

    |